Energy Efficiency on Track

 

Predictions: 

In this experiment, we slid a wooden block down an aluminum ramp and we measured how much energy was lost to kinetic friction. By making measurements of the velocity and using energy conservation, we calculated the kinetic frictional force and comparing it to the normal force to solve for the coefficient of kinetic friction, μk​

For the experiments with constant angle and varying mass, initial and final velocities provided us with an experimental efficiency of approximately 65%, this means that about 35% of the initial energy was lost because of friction. Linear regression of the kinetic friction vs. normal force data provided an experimental coefficient of kinetic friction of μk≈0.63. For experiments with constant mass and varying angles, μk was even higher, about 1.01. These are significantly higher than the range to be expected for wood on aluminum (0.3–0.6), which means other forces or measurement error had an effect on the results.

Friction was also a major contributor, especially on the inclined track. As the angle increased, the normal force decreased, but energy losses remained high. The frictional force, fk=μkN, did negative work on the block, reducing its kinetic energy. The difference between theoretical and experimental values indicates the necessity of considering all the energy losses, including friction, potential slipping, or irregular contact.

To estimate frictional energy loss, we compared initial and final kinetic energy. The dissipated energy was in agreement with the difference
ΔKE=1/2mvi^2-1/2mvf^2. This can also be employed to calculate the average frictional force back.

We estimated the unceartinty using unceartinty propogation from the measured height values and this gave us a velocity unceartinty which is about +/-0.44.  

In short, our experimentally found coefficients of kinetic friction were in the range of 0.63 +/-0.44 to 1.01 +/-0.44, indicating significant energy loss to friction. These results serve to highlight the importance of precise measurement of velocity and attention to friction in investigating systems on inclines. Though error is unavoidable, multiple trials, video analysis, and more thorough inspection of track and block surfaces would improve accuracy and move results closer to conforming with theoretical predictions.